Question #N149
A circle in the $xy$-plane has a diameter with endpoints $(2,-4)$ and $(2,14)$. What is the length of the radius of the circle?
A. 5
B. 10
C. 18
D. 20
Correct Answer is: A
The radius of a circle is half the length of its diameter. The length of the diameter can be found using the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. Substituting (2,-4) and (2,14) for $(x_1, y_1)$ and $(x_2, y_2)$ gives a distance of $\sqrt{(2-2)^2 + (14-(-4))^2} = \sqrt{0^2 + 18^2} = \sqrt{324} = 18$. Half of 18 is 9, so the radius of the circle is 9.